Spectral element filtering techniques for large eddy simulation with dynamic estimation

Spectral element methods have previously been successfully applied to direct numerical simulation of turbulent flows with moderate geometrical complexity and low to moderate Reynolds numbers. A natural extension of application is to large eddy simulation of turbulent flows, although there has been little published work in this area. One of the obstacles to such application is the ability to deal successfully with turbulence modelling in the presence of solid walls in arbitrary locations. An appropriate tool with which to tackle the problem is dynamic estimation of turbulence model parameters, but while this has been successfully applied to simulation of turbulent wall-bounded flows, typically in the context of spectral and finite volume methods, there have been no published applications with spectral element methods. Here, we describe approaches based on element-level spectral filtering, couple these with the dynamic procedure, and apply the techniques to large eddy simulation of a prototype wall-bounded turbulent flow, the plane channel, using a mixing length-based eddy viscosity subgrid-scale model. The methods outlined here may be carried over without modification to more complex geometries.